Superfast broadband has now reached three million homes and businesses as part of a government roll-out, said ministers.
The Government's Broadband Delivery UK programme has been designed to provide superfast broadband speeds of at least 24 megabits per second (Mbps) to 95 per cent of the country by 2017.
Currently, the programme is being rolled out in three phases, the first of which aims to provide all households and businesses with standard speed broadband of 2 Mbps by next year as well as superfast connections to 90 per cent of premises.
But many have said the programme needs to be delivered faster and MPs in some rural areas remain unconvinced by the claims of superfast coverage for their constituents.
Communications Minister Ed Vaizey told the BBC Radio 4 Today programme that the Government acknowledged these concerns. "There are three million homes now that have broadband that wouldn't have had broadband. We have the best broadband of the big five economies in Europe," he said.
"Often when I come on programmes like this, people will be quoted saying they haven't got broadband and they are frustrated. I completely agree with them - that is why we are doing this programme."
According to Think Broadband's speed test map of the UK, however, some parts of the West Country have broadband speeds as low as 0.89 Mbps.
Ian Liddell-Grainger, Conservative MP for Bridgwater and West Somerset, told the Financial Times: "I don't believe the numbers. In West Somerset, I should think coverage is about 40 per cent."
A packed debate in the House of Commons in June saw MPs urge ministers to accelerate the delivery of the programme. Conservative Matt Warman, the new MP for Boston and Skegness, was joined by dozens of Tory colleagues to demand swifter action in the availability of faster connections.
"The issue we discuss today is by far the most important infrastructure programme we will consider in our lifetime," said Warman, a former technology journalist. "When we talk endlessly about the vital importance of infrastructure it is very often roads and railways that we emphasis.
"When I talk to constituents it is almost always broadband that comes up as the most important infrastructure project they would like to see."
Tiverton and Honiton MP Neil Parish added that BT, whose taxpayer-supported Openreach scheme is one of the main ways of delivering broadband, needed to do more.
"BT is a very good company but it is dominant in the marketplace," he said. "There is very many good parts of the country where they are delivering very good broadband, but there are other parts of the country where they are just not delivering.
"I want to see action now to make sure BT delivers. It's all of our constituents put at disadvantage, we have got many businesses which will not get broadband probably until 2020 and beyond."
Shadow culture secretary Chris Bryant said: "This is going to be important to our economic future - it is in a sense a utility as important and as essential as electricity is. We all agree some significant progress has been made.
"But I think the symbolic fact there are so many MPs here, of all political parties, is an indication from our constituencies that we have to say to the minister not enough progress has been made."